Hello, I am currently going through theory on signals. While I am able to understand the math part of it, I am not able to fully understand how classifying a signal as energy or power is useful. Can someone clarify ... _____________________________ Posted through www.DSPRelated.com
power and energy signals
Started by ●December 19, 2013
Reply by ●December 19, 20132013-12-19
On Thu, 19 Dec 2013 09:32:30 -0600, Sharan123 wrote:> Hello, > > I am currently going through theory on signals. While I am able to > understand the math part of it, I am not able to fully understand how > classifying a signal as energy or power is useful. > > Can someone clarify ...I haven't heard that term before, but I assume that you're making a distinction between signals with finite energy vs. signals with finite power. It colors what math you can do with it. When you take the Fourier transform of a signal with finite energy you get a finite result. When you take the Fourier transform of a signal with infinite energy you get a result that goes to infinity in at least one spot. So to analyze "energy" signals you have to do all sorts of mathematical dodges so that you can get sensible results. Since any continuous signal is finite energy, you'd really like to have a way to analyze it, and since Fourier analysis is so easy and prevalent, you'd like to analyze your signal with Fourier analysis. -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
Reply by ●December 19, 20132013-12-19
On 12/19/13 10:40 AM, Tim Wescott wrote:> On Thu, 19 Dec 2013 09:32:30 -0600, Sharan123 wrote: > >> Hello, >> >> I am currently going through theory on signals. While I am able to >> understand the math part of it, I am not able to fully understand how >> classifying a signal as energy or power is useful. >> >> Can someone clarify ... > > I haven't heard that term before, but I assume that you're making a > distinction between signals with finite energy vs. signals with finite > power.i think my A.B. Carlson book calls them "power" and "energy" signals when, Tim is absolutely right, they should be called "finite power" and "finite energy".> It colors what math you can do with it.i think, for the purpose of (theoretical) analysis, the difference in the math is right at the beginning: Finite Energy signals, x(t), y(t): (square of) norm: +inf ||x||^2 = integral{ |x(t)|^2 dt } < inf -inf inner product: +inf <x,y> = integral{ x(t) conj{y(t)} dt } < inf -inf Finite Power signal, x(t), y(t): (square of) norm: +T/2 ||x||^2 = lim 1/T integral{ |x(t)|^2 dt } < inf T->inf -T/2 inner product: +T/2 <x,y> = lim 1/T integral{ x(t) conj{y(t)} dt } < inf T->inf -T/2 in all cases the norm of x(t) is the square root of the inner product x(t) with itself: ||x|| = sqrt( <x,x> ) the square of the norm is the energy of a finite energy signal and is the power of a finite power signal. you can think of the norm as a sorta r.m.s. value. same can be done to discrete-time signals x[n] and y[n]. replace integrals with summations and "T" with "N". no big deal. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 19, 20132013-12-19
"Sharan123" <99077@dsprelated> writes:> Hello, > > I am currently going through theory on signals. While I am able to > understand the math part of it, I am not able to fully understand how > classifying a signal as energy or power is useful.Sharan, It makes a difference because if you want to look at the signal in the frequency domain since the Fourier transform is an integral that only exists under certain conditions, known as the Dirichlet conditions, and a power signal violates those conditions (though there are ways to handle that problem). -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●December 19, 20132013-12-19
On Thursday, December 19, 2013 7:32:30 AM UTC-8, Sharan123 wrote:> Hello, > ... > Can someone clarify ...Some good examples are in the application Notes from Br�el & Kj�r: Choose Your Units www.bksv.com/doc/bo0438.pdf? see Page 29 of Technical review No. 3 - 1987 Signals and Units http://www.bksv.com/doc/Bv0031.pdf Dale B. Dalrymple
Reply by ●December 19, 20132013-12-19
On Thursday, December 19, 2013 10:32:30 AM UTC-5, Sharan123 wrote:> Hello, > > > > I am currently going through theory on signals. While I am able to > > understand the math part of it, I am not able to fully understand how > > classifying a signal as energy or power is useful. > > > > Can someone clarify ... > > > > _____________________________ > > Posted through www.DSPRelated.comSimple way to think of units is you have: amplitude, amplitude^2, and amplitude^2 / time typically the 2nd and 3rd are energy and power. IHTH, Clay
Reply by ●December 19, 20132013-12-19
On Thu, 19 Dec 2013 13:18:12 -0800 (PST), clay@claysturner.com wrote:>On Thursday, December 19, 2013 10:32:30 AM UTC-5, Sharan123 wrote: >> Hello, >> >> >> >> I am currently going through theory on signals. While I am able to >> >> understand the math part of it, I am not able to fully understand how >> >> classifying a signal as energy or power is useful. >> >> >> >> Can someone clarify ... >> >> >> >> _____________________________ >> >> Posted through www.DSPRelated.com > >Simple way to think of units is you have: > >amplitude, amplitude^2, and amplitude^2 / time > >typically the 2nd and 3rd are energy and power. > >IHTH, >Clay > >So, is power and energy supposed to be in units of watts and joules, respectively ? I think that may be part of Sharan123's question. I've always wondered about that too since, I would think that a load of some sort would be necessarily implied for real power or energy to take place. And, if a complex spectrum, wouldn't that be analogous to VARs in the electrical power world ? I have just always assumed that typically, a speaker and amplifier was the load if it is an audio application of DSP. But, average power is average power, etc. boB K7IQ
Reply by ●December 19, 20132013-12-19
On 12/19/13 8:55 PM, boB wrote:> > > So, is power and energy supposed to be in units of watts and joules, > respectively ? > > I think that may be part of Sharan123's question. > > I've always wondered about that too since, I would think that a load > of some sort would be necessarily implied for real power or energy to > take place.yes. i always thought of that as 1 ohm if v(t) is in volts. but the discrete-time samples are equal to dimensionless numbers that are the volts of v(t) divided by some reference voltage V_ref. you can make it joules and watts if you know what the V_ref and the assumed load in ohms. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 20, 20132013-12-20
On Thu, 19 Dec 2013 21:17:49 -0500, robert bristow-johnson <rbj@audioimagination.com> wrote:>On 12/19/13 8:55 PM, boB wrote: >> >> >> So, is power and energy supposed to be in units of watts and joules, >> respectively ? >> >> I think that may be part of Sharan123's question. >> >> I've always wondered about that too since, I would think that a load >> of some sort would be necessarily implied for real power or energy to >> take place. > >yes. i always thought of that as 1 ohm if v(t) is in volts. > >but the discrete-time samples are equal to dimensionless numbers that >are the volts of v(t) divided by some reference voltage V_ref. >>you can make it joules and watts if you know what the V_ref and the >assumed load in ohms.Yep, absolutely... Typically I see these examples and calculations in a purely software context. So, what is the impedance of 1s and 0s ? boB Washington, AC
Reply by ●December 20, 20132013-12-20
On Thu, 19 Dec 2013 23:20:44 -0800, boB wrote:> On Thu, 19 Dec 2013 21:17:49 -0500, robert bristow-johnson > <rbj@audioimagination.com> wrote: > >>On 12/19/13 8:55 PM, boB wrote: >>> >>> >>> So, is power and energy supposed to be in units of watts and joules, >>> respectively ? >>> >>> I think that may be part of Sharan123's question. >>> >>> I've always wondered about that too since, I would think that a load >>> of some sort would be necessarily implied for real power or energy to >>> take place. >> >>yes. i always thought of that as 1 ohm if v(t) is in volts. >> >>but the discrete-time samples are equal to dimensionless numbers that >>are the volts of v(t) divided by some reference voltage V_ref. >> >> >>you can make it joules and watts if you know what the V_ref and the >>assumed load in ohms. > > Yep, absolutely... > > Typically I see these examples and calculations in a purely software > context. So, what is the impedance of 1s and 0s ? > > boB Washington, ACThe "digital milliwatt" used in telephony is defined as being this exact set of mu-Law encoded values at an 8kHz sample rate: 0x1e, 0x0b, 0x0b, 0x1e, 0x9e, 0x8b, 0x8b, 0x9e There is also an A-law equivalent, which has different bits but serves the same role. Since we have a 1mW reference, digital signals can be expressed in dBm (but only in a telephony context). Regards, Allan
